Neutron scattering and scaling behavior in ${\text{URu}}_2{\text{Zn}}_{20}$ and ${\text{YbFe}}_2{\text{Zn}}_{20}$

The dynamic susceptibility ${\chi }^{″}\left(\Delta E\right)$, measured by inelastic neutron-scattering measurements, shows a broad peak centered at $E_{max}=15\text{meV}$ for the cubic actinide compound ${\text{URu}}_2{\text{Zn}}_{20}$ and 7 meV at zone center and at the (1/2, 1/2, 1/2) zone boundary for the rare-earth counterpart compound ${\text{YbFe}}_2{\text{Zn}}_{20}$. For ${\text{URu}}_2{\text{Zn}}_{20}$, the low-temperature susceptibility and magnetic specific-heat coefficient $\gamma =C_{mag}/T$ take the values $\chi =0.011\text{emu}/\text{mole}$ and $\gamma =190\text{mJ}/\text{mole}{\text{K}}^2$ at $T=2\text{K}$. These values are roughly three times smaller, and $E_{max}$ is three times larger, than recently reported for the related compound ${\text{UCo}}_2{\text{Zn}}_{20}$, so that $\chi$ and $\gamma$ scale inversely with the characteristic energy for spin fluctuations, $T_{sf}=E_{max}/k_B$. While $\chi \left(T\right)$, $C_{mag}\left(T\right)$, and $E_{max}$ of the $4f$ compound ${\text{YbFe}}_2{\text{Zn}}_{20}$ are very well described by the Kondo impurity model, we show that the model works poorly for ${\text{URu}}_2{\text{Zn}}_{20}$ and ${\text{UCo}}_2{\text{Zn}}_{20}$, suggesting that the scaling behavior of the actinide compounds arises from spin fluctuations of itinerant $5f$ electrons.

Figure 1

(Color online) (a) Magnetic susceptibility $\chi \left(T\right)$ for ${\text{URu}}_2{\text{Zn}}_{20}$. The lines are Curie-Weiss fits. (b) Specific heat $C/T$ vs $T$ of ${\text{URu}}_2{\text{Zn}}_{20}$. Insets: susceptibility and specific heat of ${\text{UCo}}_2{\text{Zn}}_{20}$; the data are from Bauer et al. (Ref. 11).

Figure 2

(Color online) Low-temperature dynamic susceptibility ${\chi }^{″}$ vs $\Delta E$ of ${\text{URu}}_2{\text{Zn}}_{20}$. Error bars in all figures represent $\pm \sigma$. (a) Pharos data at $T=7\text{K}$ $\left(E_i=35\text{meV}\right)$. (b) LRMECS data at $T=10\text{K}$ $\left(E_i=60\text{meV}\right)$. The lines represent Lorentzian fits with $E_0=12.4\pm 0.6\text{meV}$ and $\Gamma =8.9\pm 0.8\text{meV}$. Inset: low-temperature dynamic susceptibility of ${\text{UCo}}_2{\text{Zn}}_{20}$; the data are from Bauer et al. (Ref. 11). The line is a Lorentzian fit with $E_0=2.2\pm 0.5\text{meV}$ and $\Gamma =4.8\pm 0.2\text{meV}$. The arrows indicate the peak positions predicted by the AIM for $N_J=10$ (See Table ).

Figure 3

(Color online) (a) Specific heat $C_{mag}\left(T\right)$ [from Torikachvili et al. (Ref. 6) and (b) magnetic susceptibility ${\chi }_{mag}\left(T\right)$ for ${\text{YbFe}}_2{\text{Zn}}_{20}$. (c) The inelastic neutron-scattering spectra of ${\text{YbFe}}_2{\text{Zn}}_{20}$ at two different $\mathbf{Q}$ in the Brillouin zone. The nonmagnetic scattering has been subtracted, as described in the text. The results show little $\mathbf{Q}$dependence. The lines are fits, for the $J=7/2$ case, to Rajan’s predictions for $C_{mag}$ and ${\chi }_{mag}$ and to Cox’s predictions for ${\chi }^{″}\left(\Delta E\right)/{\chi }^{″}\left(E_{max}\right)$. In all three cases, there is only one common adjustable parameter $T_0$, set to the value 69 K to give the best agreement with experiment.

Figure 4

(Color online) (a) Magnetic susceptibility $\chi \left(T\right)$, (b) magnetic specific heat $C_{mag}\left(T\right)$, and (c) entropy $S_{mag}\left(T\right)$ for ${\text{URu}}_2{\text{Zn}}_{20}$; the insets show the same quantities for ${\text{UCo}}_2{\text{Zn}}_{20}$ (Ref. 11). The lines are fits using Rajan’s predictions for $J=9/2$. The open symbols in (b) and (c) represent data corrected for the energy of the Einstein mode at 8 (7) meV in the U (Th) compounds (Ref. 24). (d): The dynamic susceptibility ${\chi }^{″}\left(\Delta E\right)/{\chi }^{″}\left(E_{max}\right)$ of ${\text{URu}}_2{\text{Zn}}_{20}$; the inset shows the data for ${\text{UCo}}_2{\text{Zn}}_{20}$. The lines are obtained using Cox’s results, as explained in the text.

Figure 5

(a) The INS spectra of ${\text{URu}}_2{\text{Zn}}_{20}$ and ${\text{ThCo}}_2{\text{Zn}}_{20}$ taken on Pharos with incident energies $E_i=400$ and 700 meV. The diamond is the estimated magnetic scattering ${\chi }^{″}$, obtained as described in the text. (b) The INS spectra of ${\text{URu}}_2{\text{Zn}}_{20}$ in the energy range 0.1–4 meV taken on DCS with incident energies $E_i=2.3$ and 7.1 meV. The near equality of the high-$Q$ and low-$Q$ scattering suggests that all the scattering observed in this energy range is due to background.